Geodesic
Fixed point theorems of $G$-fuzzy contractions in fuzzy metric spaces endowed with a graph
Communications in Mathematics, Tome 22 (2014) no. 1, pp. 1-12 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $(X,M,\ast )$ be a fuzzy metric space endowed with a graph $G$ such that the set $V(G)$ of vertices of $G$ coincides with $X$. Then we define a $G$-fuzzy contraction on $X$ and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.
Let $(X,M,\ast )$ be a fuzzy metric space endowed with a graph $G$ such that the set $V(G)$ of vertices of $G$ coincides with $X$. Then we define a $G$-fuzzy contraction on $X$ and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.
Classification : 47H10, 54A40, 54E40, 54H25
Keywords: graph; partial order; fuzzy metric space; contraction; fixed point 
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Shukla, Satish. Fixed point theorems of $G$-fuzzy contractions in fuzzy metric spaces endowed with a graph. Communications in Mathematics, Tome 22 (2014) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/COMIM_2014_22_1_a0/

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